Well, that was an exercise in futility.
I figured I ought to make a Taobao account and quit bugging my one friend who has one, every time I want to buy one of Quad's voicebanks or something. It let me sign up with an international phone number just fine. But immediately after making an account, trying to log in gave me an error that my account was frozen.
Googled this, found a reddit discussion about getting this sorted by verifying the account, usually by calling the help line. Other comments mentioned verifying it through Alipay, which you need to use to shop on Taobao anyway afaik. So I decided to try that first.
Downloaded Alipay. Tried to make an account with my number. Said I already had an account, no need. Guess it's linked to Taobao, or else I've tried in the past and have no memory of it (this is not unusual for my shoddy memory, it's more plausible than it sounds). Sign into the account, go to add a card. Detects my card type fine, but it wants some kind of ID verification first. Makes sense. Passport number? Huh. Let's try verifying the account itself with some other type of ID before adding a card, under settings. Except, there is no other ID type available. Passports or bust. I do not have a passport.
Fine. Google applying for passports in my state. Processing time is 4-6 weeks, and the application and acceptance fees altogether are almost $200. Yeah. Never mind. I don't want it that bad.
Moral of the story is, if you already have a passport and want to order stuff on Taobao, it should be pretty easy to make an Alipay account and then use that to verify your Taobao. If you do not have a passport, sucks to suck